Question

in reperul cartezian xoy se considera punctele a(2 -5) b(-3 5). determinati coordonatele punctului M(xm,ym) stiind ca BM=1/5AM

Answer 1

$AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}}=5\sqrt{5}$

$AB=AM+BM=AM+\frac{1}{5}*AM=\frac{6}{5}*AM => AM=\frac{25\sqrt{5} }{6}$

$AM=\sqrt{(x_M-x_A)^2+(y_M-y_A)^2}}=\frac{25\sqrt{5}}{6} \\\((x_M-x_A)^2+(y_M-y_A)^2}=\frac{3125}{36}=$

$BM=\frac{1}{5} *AM=\frac{5\sqrt{5} }{6}\\(x_M-x_B)^2+(y_M-y_B)^2}=\frac{125}{36}$